103 + 2 = 105
It is 2.
3 and 2 over 7 = ( 3*7 + 2 )/ 7 = 23/7 7 and 1 over 15 = ( 7*15 + 1 ) / 15 = 106/15 The least common multiple of 7 and 15 is 105 So, 23/7 + 106/15 = 23*15 / 105 + 106*7 / 105 = 345 / 105 + 742 / 105 = 1087 / 105 = (1050 + 37 ) / 105 = 10 and 37 over 105
If 3x - 1 = 11 what is the value of x 2 + x?
- If 3X - 1 = 11, what is the value of X^2 + X?
105
103 + 2 = 105
It is 2.
3 and 2 over 7 = ( 3*7 + 2 )/ 7 = 23/7 7 and 1 over 15 = ( 7*15 + 1 ) / 15 = 106/15 The least common multiple of 7 and 15 is 105 So, 23/7 + 106/15 = 23*15 / 105 + 106*7 / 105 = 345 / 105 + 742 / 105 = 1087 / 105 = (1050 + 37 ) / 105 = 10 and 37 over 105
It has to be between zero and 2, but the exact value depends on the value of Θ .
If 3x - 1 = 11 what is the value of x 2 + x?
To find the exact value of tan 105°. First, of all, we note that sin 105° = cos 15°; and cos 105° = -sin 15°. Thus, tan 105° = -cot 15° = -1 / tan 15°. Using the formula tan(α - β) = (tan α - tan β) / (1 + tan α tan β); and using, also, the familiar values tan 45° = 1, and tan 30° = ½ / (½√3) = 1/√3 = ⅓√3; we have, tan 15° = (1 - ⅓√3) / (1 + ⅓√3); whence, cot 15° = (1 + ⅓√3) / (1 - ⅓√3) = (√3 + 1) / (√3 - 1) {multiplying through by √3} = (√3 + 1)2 / (√3 + 1)(√3 - 1) = (3 + 2√3 + 1) / (3 - 1) = (4 + 2√3) / 2 = 2 + √3. Therefore, tan 105° = -cot 15° = -2 - √3, which is the result we sought. We are asked the exact value of tan 105°, which we gave above. We can test the above result to 9 decimal places, say, by means of a calculator: -2 - √3 = -3.732050808; and tan 105° = -3.732050808; thus indicating that we have probably got the right result.
- If 3X - 1 = 11, what is the value of X^2 + X?
105 is divisible by 5 because it ends in a 5. 105/5 = 21, so 5*21=105. Since 21 = 3*7, and 5*3=15 and 5*7=35, 15*7 = 105 and 35*3 = 105 too. Also, 105 * 1 = 105. 210 * 1/2 = 105, 315 * 1/3 = 105, etc. Here I multiplied 105 by 2 or 3 and then multiplied back by 1/2 or 1/3.
2 x 0 x 1 + 1 = 0 + 1 = 1
2(10)+1
n = 1/2